These may be petechiae or blood leaking through the blood vessels due to the pressure you apply on the arm when lying down. Petechiae are tiny reddish to purplish spots that appear on the skin
In the absence of any increase in the size of these spots and also without other associated symptoms of headaches, nose bleed or gum bleed, then there is no need to worry about this. Try to modify your sleeping position. Do not lie on your arms when sleeping as this may cause some nerve related problems and muscle pains.
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